Answer
The distance between nodes is $~~3.0~cm$
Work Step by Step
We can write a general expression for the standing wave:
$y'(x,t) = [(2y_m) sin ~(kx)]~cos~\omega t$
In the equation for the standing wave, we can see that $~~k = \frac{\pi}{3} cm^{-1}$
We can find $\lambda$:
$\lambda = \frac{2\pi}{k}$
$\lambda = \frac{2\pi}{\frac{\pi}{3} cm^{-1}}$
$\lambda = 6.0~cm$
Since the distance between nodes is $\frac{\lambda}{2}$, the distance between nodes is $~~3.0~cm$
